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NDA 2013
Exam
NDA
Year
2013
Subject
Mathematics
Chapter
Differentiation

NDA 2013 · Mathematics · Differentiation

The derivative of ^2 x with respect to ^2 x is

The derivative of sec⁡2x\sec ^2 x with respect to tan⁡2x\tan ^2 x is

Options

  1. A11
  2. B22
  3. C2sec⁡xtan⁡x2 \sec x \tan x
  4. D2sec⁡2xtan⁡x2 \sec ^2 x \tan x

Correct answer

A. 11

Step-by-step solution

v=sec⁡2x,z=tan⁡2xdvdz=dv/dxdz/dx=2sec⁡x⋅sec⁡xtan⁡x2tan⁡x⋅sec⁡2x=1\begin{aligned} & v=\sec ^2 x, z=\tan ^2 x \\ & \frac{d v}{d z}=\frac{d v / d x}{d z / d x}=\frac{2 \sec x \cdot \sec x \tan x}{2 \tan x \cdot \sec ^2 x}=1\end{aligned}
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